416 research outputs found
Second-Order Belief Hidden Markov Models
Hidden Markov Models (HMMs) are learning methods for pattern recognition. The
probabilistic HMMs have been one of the most used techniques based on the
Bayesian model. First-order probabilistic HMMs were adapted to the theory of
belief functions such that Bayesian probabilities were replaced with mass
functions. In this paper, we present a second-order Hidden Markov Model using
belief functions. Previous works in belief HMMs have been focused on the
first-order HMMs. We extend them to the second-order model
A compact statistical model of the song syntax in Bengalese finch
Songs of many songbird species consist of variable sequences of a finite
number of syllables. A common approach for characterizing the syntax of these
complex syllable sequences is to use transition probabilities between the
syllables. This is equivalent to the Markov model, in which each syllable is
associated with one state, and the transition probabilities between the states
do not depend on the state transition history. Here we analyze the song syntax
in a Bengalese finch. We show that the Markov model fails to capture the
statistical properties of the syllable sequences. Instead, a state transition
model that accurately describes the statistics of the syllable sequences
includes adaptation of the self-transition probabilities when states are
repeatedly revisited, and allows associations of more than one state to the
same syllable. Such a model does not increase the model complexity
significantly. Mathematically, the model is a partially observable Markov model
with adaptation (POMMA). The success of the POMMA supports the branching chain
network hypothesis of how syntax is controlled within the premotor song nucleus
HVC, and suggests that adaptation and many-to-one mapping from neural
substrates to syllables are important features of the neural control of complex
song syntax
Networked buffering: a basic mechanism for distributed robustness in complex adaptive systems
A generic mechanism - networked buffering - is proposed for the generation of robust traits in complex systems. It requires two basic conditions to be satisfied: 1) agents are versatile enough to perform more than one single functional role within a system and 2) agents are degenerate, i.e. there exists partial overlap in the functional capabilities of agents. Given these prerequisites, degenerate systems can readily produce a distributed systemic response to local perturbations. Reciprocally, excess resources related to a single function can indirectly support multiple unrelated functions within a degenerate system. In models of genome:proteome mappings for which localized decision-making and modularity of genetic functions are assumed, we verify that such distributed compensatory effects cause enhanced robustness of system traits. The conditions needed for networked buffering to occur are neither demanding nor rare, supporting the conjecture that degeneracy may fundamentally underpin distributed robustness within several biotic and abiotic systems. For instance, networked buffering offers new insights into systems engineering and planning activities that occur under high uncertainty. It may also help explain recent developments in understanding the origins of resilience within complex ecosystems. \ud
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Cell Lineage Determination in State Space: A Systems View Brings Flexibility to Dogmatic Canonical Rules
Endogenous Hidden Markov Regimes in Operational Loss Data: Application to the Recent Financial Crisis
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The effect of asymmetries on stock index return value-at-risk estimates
It is widely accepted that equity return volatility increases more following negative shocks rather than positive shocks. However, much of value-at-risk (VaR) analysis relies on the assumption that returns are normally distributed (a symmetric distribution). This article considers the effect of asymmetries on the evaluation and accuracy of VaR by comparing estimates based on various models
Biophysics and systems biology
Biophysics at the systems level, as distinct from molecular biophysics, acquired its most famous paradigm in the work of Hodgkin and Huxley, who integrated their equations for the nerve impulse in 1952. Their approach has since been extended to other organs of the body, notably including the heart. The modern field of computational biology has expanded rapidly during the first decade of the twenty-first century and, through its contribution to what is now called systems biology, it is set to revise many of the fundamental principles of biology, including the relations between genotypes and phenotypes. Evolutionary theory, in particular, will require re-assessment. To succeed in this, computational and systems biology will need to develop the theoretical framework required to deal with multilevel interactions. While computational power is necessary, and is forthcoming, it is not sufficient. We will also require mathematical insight, perhaps of a nature we have not yet identified. This article is therefore also a challenge to mathematicians to develop such insights
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